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# [1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/

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Intern
Joined: 09 Sep 2012
Posts: 33
Location: United States
[1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/ [#permalink]

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11 Oct 2012, 20:50
1
KUDOS
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (01:00) wrong based on 5 sessions

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Guys plz help me with the question below

[1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/100]

a)52
b)53
c)54
d)55
e)none of these

Thanks
[Reveal] Spoiler: OA
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7453
Location: Pune, India
Re: [1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/ [#permalink]

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11 Oct 2012, 21:41
154238 wrote:
Guys plz help me with the question below

[1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/100]

a)52
b)53
c)54
d)55
e)none of these

Thanks

There is something wrong in the answer choices or the question (or the answer is (E)).

Ignore the 1/2s right now.
You have 1/100 and you have 99/100 in the series. When you add them, you will get 1.
Similarly, you have 2/100 and 98/100. This will again give you 1.
This will continue till 49/100 and 51/100.
So you have a total of 49.
You are left with 5 terms: 50/100 + 100/100 + 101/100 + 102/100 + 103/100 which add to apprx 4.5
Now you have a 103 times 1/2 which adds up to 51.5

So the total is 49 + 4.5 + 51.5 = 105 apprx
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7453 Location: Pune, India Re: [1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/ [#permalink] ### Show Tags 11 Oct 2012, 21:46 You can also use the concept of sum of first n integers here. Sum of first n integers = n(n+1)/2 Take all 1/2s together and take out 1/100 common out of the rest of the terms. 103*(1/2) + (1/100)(1 + 2 + 3 + 4 ....+ 103) = 103/2 + (1/100) (103*104)/2 = 105 apprx _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Intern
Joined: 09 Sep 2012
Posts: 33
Location: United States
Re: [1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/ [#permalink]

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11 Oct 2012, 22:22
VeritasPrepKarishma wrote:
154238 wrote:
Guys plz help me with the question below

[1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/100]

a)52
b)53
c)54
d)55
e)none of these

Thanks

There is something wrong in the answer choices or the question (or the answer is (E)).
Ignore the 1/2s right now.
You have 1/100 and you have 99/100 in the series. When you add them, you will get 1.
Similarly, you have 2/100 and 98/100. This will again give you 1.
This will continue till 49/100 and 51/100.
So you have a total of 49.
You are left with 5 terms: 50/100 + 100/100 + 101/100 + 102/100 + 103/100 which add to apprx 4.5
Now you have a 103 times 1/2 which adds up to 51.5

So the total is 49 + 4.5 + 51.5 = 105 apprx

Even i feel that the answer given was incorrect. Thanks for your help

Cheers
Re: [1/2+1/100] + [1/2+2/100] + [1/2+3/100] + ...... + [1/2+103/   [#permalink] 11 Oct 2012, 22:22
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